Evaluate and show your work:
9P4 using the nPr formula
9P4 = 9! / 4!(9-4!)
now simplify
3024?
To evaluate 9P4 using the nPr formula, we need to use the formula:
nPk = n! / (n - k)!
Here, n represents the total number of items in the set, and k represents the number of items being selected.
In this case, n = 9 and k = 4, so we have:
9P4 = 9! / (9 - 4)!
Let's calculate this step by step:
Step 1: Determine (9 - 4)!
(9 - 4)! = 5!
Step 2: Calculate 5!
5! = 5 x 4 x 3 x 2 x 1 = 120
Step 3: Determine 9!
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
Step 4: Substitute the values into the formula
9P4 = 362,880 / 120
Step 5: Simplify the fraction
9P4 = 3,024
Therefore, 9P4 = 3,024.
To evaluate 9P4 using the nPr formula, we need to use the formula for permutation:
nP r = n! / (n - r)!
Let's plug in the values of n and r:
n = 9
r = 4
9P4 = 9! / (9 - 4)!
Now, let's calculate the factorials:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
(9 - 4)! = 5!
Calculating the factorials, we have:
9! = 362,880
5! = 120
Now, let's substitute these values back into the formula:
9P4 = 362,880 / 120
Using division, we have:
9P4 = 3024
Therefore, the value of 9P4 is 3024.
And that is how we evaluate 9P4 using the nPr formula and calculate the factorials along the way.